In optical communication networks, electro-optic devices are routinely employed to modulate optical signals through electro-optic interaction. With reference to FIGS. 1A and 1B, a prior-art electro-optic device 100 known as a dual-drive Mach-Zehnder (DDMZ) modulator is suitable for long reach and very long reach applications. The electro-optic device 100 includes an input port 101, which is followed in an optical-signal transit direction by a Mach-Zehnder interferometer (MZI) 102 having independently modulated arms, which is followed by an output port 103. Similar electro-optic devices are disclosed in U.S. Pat. No. 6,980,706 to Sugiyama, issued on Dec. 27, 2005, in U.S. Pat. No. 6,678,428 to Seino, et al., issued on Jan. 13, 2004, in U.S. Pat. No. 6,192,167 to Kissa, et al., issued on Feb. 20, 2001, and in U.S. Pat. No. 5,074,631 to Hamano, et al., issued on Dec. 24, 1991, which are incorporated herein by reference.
The electro-optic device 100 comprises an electro-optic substrate 110, which includes two optical waveguides 111 for propagating two optical signals, as part of the MZI 102. Two radio-frequency (RF) signal electrodes 120 for propagating two RF signals to modulate the two optical signals through electro-optic interaction are supported by the electro-optic substrate 110. RF-ground electrodes for grounding, which are omitted from FIGS. 1A and 1B for clarity, are also supported by the electro-optic substrate 110.
The RF-signal electrodes 120 each include an input segment 121 for receiving an RF signal, an interaction segment 122, which follows the input segment 121 in an RF-signal transit direction, for producing an electric field in one of the two optical waveguides 111 in response to the RF signal, and an output segment 123 which follows the interaction segment 122 in the RF-signal transit direction, for transmitting the RF signal. In some instances, the electro-optic substrate 110 is of z-cut LiNbO3, and the waveguides 111 are each disposed directly under an interaction segment 122, as illustrated in FIG. 1. In other instances, the electro-optic substrate 110 is of x-cut LiNbO3, and the waveguides 111 are each disposed between the interaction segment 122 of an RF-signal electrode 120 and an RF-ground electrode. The input segments 121 are each connected to a respective input bond pad 124, and the output segments 123 are each connected to a respective output bond pad 125.
With particular reference to FIG. 1B, the input segments 121 of the RF-signal electrodes 120 are arranged in a branched pattern 150 followed in the RF-signal transit direction by a parallel-bend pattern 160. Advantageously, this arrangement allows matching of RF-signal transit times of the input segments 121 and near matching of RF-signal losses of the input segments 121, as required for more complex modulation formats.
The branched pattern 150 has two branches of different lengths, each formed by a sub-segment of one input segment 121a or 121b. At one end of the branched pattern 150, the input bond pads 124 are spaced at a separation S1, which is, typically, set to a minimum value providing an acceptable level of electrical crosstalk. At the other end of the branched pattern 150, the parallel-bend pattern 160, which connects the input segments 121 to the interaction segments 122, includes a final sub-segment of each input segment 121. The final sub-segments of the input segments 121 are approximately parallel to one another and each include a final bend. The final bend of one input segment 121a is of radius R3, and the final bend of the other input segment 121b is of radius R2, such that the final sub-segments of the input segments 121 are spaced at a separation Sb, as are the interaction segments 122. The radius R2 is set to a minimum value providing an acceptable level of RF-signal bend loss, and the separation Sb is set to a minimum value providing an acceptable level of electro-optic crosstalk.
In the branched pattern 150, the sub-segments of the input segments 121 each include a first bend, a straight section, and a second bend. The first bends of the sub-segments of both input segments 121 are of radius R1, the straight section of the sub-segment of one input segment 121a is of length L1, the straight section of the sub-segment of the other input segment 121b is of length L2, and the second bends of the sub-segments of both input segments 121 are of radius R2. As is the radius R2, the radius R1 is set to a minimum value providing an acceptable level of RF-signal bend loss.
The length difference (L2−L1) between the straight sections of the branched pattern 150 introduces an electrical-length difference ΔLe,s1 of the branched pattern 150, which is given by Equation (1):ΔLe,s1=ns(L2−L1),   (1)where ns is a microwave index of refraction of for the straight sections of the electro-optic substrate 110. Likewise, the radius difference (R3−R2) between the final bends of the parallel-bend pattern 160 introduces an electrical-length difference ΔLe,b1 of the parallel-bend pattern 160, which is given by Equation (2):
                                          Δ            ⁢                                                  ⁢                          L                              e                ,                                  b                  ⁢                                                                          ⁢                  1                                                              =                                    π              2                        ⁢                                          n                b                            ⁡                              (                                                      R                    3                                    -                                      R                    2                                                  )                                                    ,                            (        2        )            where nb is a microwave index of refraction for the bends of the electro-optic substrate 110.
Note that, in some instances, the microwave index of refraction ns for the straight sections may not equal the microwave index refraction nb for the bends. For example, when the electro-optic substrate 110 is of x-cut LiNbO3, the microwave index of refraction nz for an RF-signal propagating along the z-axis of the crystal is different from the microwave index of refraction nx for an RF-signal propagating along the y-axis of the crystal. In such instances, if the straight sections are aligned with the y-axis, then the microwave index of refraction ns for the straight sections is equal to ny, and the microwave index of refraction nb for the bends is equal to (ny+nz)/2.
As the radius R3 is equal to a sum of the radius R2 and the separation Sb, the radius difference in Equation (1) may be replaced by the separation Sb, giving Equation (3):
                              Δ          ⁢                                          ⁢                      L                          e              ,                              b                ⁢                                                                  ⁢                1                                                    =                              π            2                    ⁢                      n            b                    ⁢                                    S              b                        .                                              (        3        )            
To match the electrical lengths of the input segments 121, the electrical-length difference of the branched pattern 150 is set to equal the electrical-length difference of the parallel-bend pattern 160, giving Equation (4):
                                          L            2                    -                      L            1                          =                              π            2                    ⁢                                    n              b                                      n              s                                ⁢                                    S              b                        .                                              (        4        )            As required by the geometry of the branched pattern 150, the lengths L1 and L2 must also satisfy Equation (5):L1+L2+2R1+2R2+Sb=S1.   (5)
Therefore, the lengths L1 and L2 may be uniquely determined by solving Equations (4) and (5) simultaneously, in order to match the electrical lengths of the entire input segments 121. Matching of the electrical lengths of the input segments 121 entails that the input segments 121 have substantially equivalent RF-signal transit times, ensuring that the two RF signals have an RF-signal timing skew of substantially zero upon reaching the interaction segments 122 after propagating through the input segments 121.
Furthermore, RF-signal propagation losses of the input segments 121 are nearly matched, because of the near matching of physical lengths that accompanies matching of the electrical lengths of the input segments 121. Additional RF-signal bend losses of the input segments 121 are nearly matched by including the same number of bends of similar radii in the input segments 121. Thus, the input segments 121 have substantially equivalent RF-signal losses.
The electro-optic devices disclosed in U.S. Pat. Nos. 6,980,706, 6,678,428, and in U.S. Pat. No. 6,192,167 have alternative designs that likewise provide an RF-signal timing skew of substantially zero. However, all of the prior-art electro-optic devices mentioned heretofore comprise only two RF-signal electrodes.
An object of the present invention is to overcome the shortcomings of the prior art by providing an electro-optic device comprising three or more RF-signal electrodes including input segments arranged to allow matching of RF-signal transit times of the input segments and near matching of RF-signal losses of the input segments. Advantageously, the input segments of the three or more RF-signal electrodes are arranged in a fractal pattern followed in an RF-signal transit direction by a parallel-bend pattern.
Other types of devices comprising electrodes arranged in different fractal patterns are disclosed in U.S. Pat. No. 7,551,094 to Veerasamy, issued on Jun. 23, 2009, in U.S. Pat. No. 7,283,290 to Pannell, et al., issued on Oct. 16, 2007, in U.S. Pat. No. 7,227,293 to Huang, et al., issued on Jun. 5, 2007, in U.S. Pat. No. 7,030,460 to Chu, et al., issued on Apr. 18, 2006, in U.S. Pat. No. 5,394,490 to Kato, et al., issued on Feb. 28, 1995, and in U.S. Pat. No. 5,309,001 to Watanabe, et al., issued on May 3, 1994, which are incorporated herein by reference.